The generator matrix

 1  0  1 X^2+X  1 X^2+2  1 X+2  1  0  1 X^2+X  1 X^2+2  1  2 X+2
 0  1 X^2+X  1 X^2+2  1 X+2  1  0  1 X^2+X  1 X^2+2  1 X+2  2  1
 0  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  2

generates a code of length 17 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+318x^16+128x^18+64x^20+1x^32

The gray image is a code over GF(2) with n=136, k=9 and d=64.
This code was found by Heurico 1.16 in 82.1 seconds.